In this dissertation I argue that political representatives have duties to be responsive to public opinion in their policy decisions. The existence of this duty, I claim, is a basic requirement of a truly democratic system of government. In chapter 2, I show that several standard versions of democratic legitimacy require political representatives to ``respect'' public opinion. However, I argue that a particular version of political legitimacy, based upon popular sovereignty and the importance of self-governance, provides an especially useful background for understanding what this ``respect'' must mean. In chapter 3, I argue that respecting public opinion requires political representatives to integrate public opinion information into their policy decisions. According to one of the standard views of political representation, the liberal conception, representatives deciding between policy alternatives should balance what they believe to be in the interests of the public against public opinion. I argue that this is the only adequate theory of political representation. Although this view of political representation is often discussed in the literature, it is less often given a mathematically precise form. Therefore, I present a formal model of such a balancing procedure, and this reveals several important formal requirements that a conception of public opinion must satisfy; most importantly, it must account for instability in the expression of public opinion, individual differences in opinion strength, and it must be representable along a cardinal scale. Standard measures of public opinion do not satisfy these requirements. I argue that if such a model of public opinion cannot be formulated, then the liberal conception of political representation is incoherent. In chapters 4 and 5, I present a model of public opinion based upon Thurstonian scaling techniques that fulfills the necessary formal requirements. Finally, in chapter 6, I discuss several important implications this model has for the measurement of public opinion, the use of public opinion by political representatives in policy deliberation, and other problems in social choice theory.